You're right that I forgot about the mega-Gateway. So... linking does give an enormous advantage.

But, if four women who couldn't even be Accepted can almost match what Rand can do, why the hell can't three or four average Aes Sedai handle him?

We can explain away the shielding by saying that its a case of women linking to shield a man (though it is highly unsatisfactory, since Lanfear was almost able to shield Rand, and four average Sisters should be able to exceed her considerably when linked), but why then was Guiare Amalasan able to tackle six sisters? They must have had a simply enormous advantage over him, linked.

I can think of one answer, though I'm by no means saying this has to be it... Maybe a circle of thriteen is special... maybe it allows for a degree of precision that no other circle can match.

There's some textual support for this. For example, Egwene, in a link and using a powerful sa'angreal, thinks that a circle fo thirteen could stop her. That would be plumb impossible unless a circle of 13 gives a much greater advantage than smaller circles (like Egwene's) do.

This also explains why even the strongest man can be stopped by 13 of the weakest of women. The number of women in the circle gives them an awesome advantage.